1. بسم الله الرحمن الرحيم

2. Chapter 12
Signal processing

3. Signal processing refers to analog and/or digital manipulation of signal
Image processing is a form of signal processing in which the manipulations are performed on digitized image
Aliasing may happens when analog signal is digitized and again the digitized signal converted to analog

4. Sequences of events in SE

5. Time requirements
Frequency encoding step takes about 10ms(4-8ms for high field and 16-30ms in low field)
Phase encoding step takes 1-5ms
Each RF pulse (with a Gz gradient) takes 2-10ms
Time spend from center of 90 degree pulse to the end echo readout is:
TE+1/2sampling time)=TE+1/2Ts
Active time=TE+1/2Ts+To
Time spend to obtain one slice image =Ny(number of phase encoding)xTR

6. The center of the k-space always contain the weakest phase encoding gradient and hence most signal
The periphery of k-space contain highest phase encoding gradient and hence weakest signal

7. Time spend to obtain one slice image =Ny(number of phase encoding)xTR

8. Multi slice technique

9. Each slice has its own k-space
Max NO of Slices(coverage)=TR/(Active time)
orTR/(TE+1/2Ts+to)
Each slice has its own k-space

10. Aliasing
when analog signal is digitized and again the digitized signal converted to analog may happen
UndersamplingAlising

11. Sampling Theorem (Nyquist law)
If ωmax is the maximum frequency in the signal, the sampling rate must be at least twice the maximum frequency to avoid aliasing.
ωsampling=1/ΔTs≥2ωmax
Ts=Nx. ΔTs=256x ΔTs
In a composite signal minimum sampling should be at least two times the maximum frequency present in the sample

13. Bandwidth(BW)=2(ωmax)=1/ΔTs
In MRI imaging; to reduce sampling time; minimum possible sampling of the signal is performed therefore:
Bandwidth(BW)=2(ωmax)=1/ΔTs
ΔTs=Ts/Nx=8ms/256=
BW=1/ ΔTs=1/ =32kHz=±16kHz
In MRI k space is the digitized version of received signal
A minimum of two samples/cycle is taken and is put in data space

14. Signal to Noise ratio (SNR)

15. Chapter 13
Data space

16. Where dose k-space come from
K-space derived from data space
It is a digitized version of data space
The x axis is spatial frequency
It has 256 phase encoding steps on y axis (+127 to -127) and 256 frequency on x-axis
Each line in the data space contain signal from entire slice
In the center row and column we put the signal with no phase encoding gradient (in x and y direction) hence max signal

17. The time taken to go from one row to another is TR
The time taken to go from one point in a row to another is ΔTs
The time taken to fill one row of data space is:
Ts =(ΔTs )(Nx)=(50ms)(256)=8.12ms
The time taken to fill one column of data space is NyxTR (for TR=500ms and Ny=256); it is about 2min

18. Motion artifact The time to fill one row is about 8ms
The time to fill one column is about 2 min
The motion artifact is mainly in y direction or in phase encoding direction

19. Properties of K space
1-The center of data space contains maximum signal
2-The maximum amplitude occurs in the center row
3-In y direction because of phase encoding gradient
4-In x direction because of rephasing and dephasing

20. Image of k space
The k space appear as a series of concentric rings of signal intensities oscillating from max to min
The intensities on the center is max and decrease when goes to periphery

21. Edge of k space The detail information provides by periphery data
The is no absolute relation between center data and center of the image

22. K space symmetry
Image can be constructed from ½ (1/2NEX) and ¼ (1/4NEX) of the data

23. Pulse sequence diagram
Chapter 14
Pulse sequence diagram

24. Pulse sequence diagram (PSD)
PSD of SE
After Gz to refocus the spins a negative pulse is applied
Crusher gradients are applied at each sides of 180 pulse to achieve more accurate refocusing at time TE

25. When apply Gx when we are reading the echo, we end up dephasing everything
To get a good signal during Gx, a negative gradient with area equal to ½ Gx is applied before Gx

26. Pre Gx gradient can be positive if it comes before 180 focussing pulse
In this case spins defase in positive direction but with 180degree pulse they reverse

27. Chapter 15
Field of View (FOV)

28. FOV: desired part of the body under investigation.
FOV depends on:
1-BW
2-Gradients

29. FOV FOV is selected by operator
FOV depends on BW and Gradients. In x direction:
Bx=(Gx).x
γ.Bx= γ.(Gx).x
fx=γ.(Gx)x
fmax=γ.(Gx)FOV/2
-fmax=-γ.(Gx)FOV/2
+fmax to fmax=2fmax=BW
BW=γ.(Gx)FOV
FOVx=BW/γ.Gx
To FOV BW
Gradient

30. What is the min possible FOV:
FOVmin=BWmin/ γ Gmax
BWmin and Gmax are machin dependent. For Echospeed Plus 1.5T scanner:
Gmax=23mT/m
BWmin=±4kHz=8kHz
Therefore FOVmin=0.8cm

31. Chapter 16
K space Final Frontier

32. What is the dimensions of the k-space matrix
The data matrix of the image is very asymmetric
Its y direction is taken in Ny.TR which is about several min
Its x direction is about 8ms

33. Δkx =γ(MHz/Tesla).Gx(miliTesla/m) .ΔTs (ms)
We had FOVx=BW/γ.Gx
We know that BW=1/ΔTs
Therefore FOVx=BW/γ.Gx=1/ γ.Gx ΔTs
Or : 1/FOVx= γ.Gx ΔTs
Term γ.Gx ΔTs is denoted Δkx hence
Δkx =γ(MHz/Tesla).Gx(miliTesla/m) .ΔTs (ms)
Δkx (cycle/m)=1/FOV

34. Main thing is: Δkx(cycle/m)=1/FOV Δx=pixel size in image
Δk=pixel size in k space
X=FOVx=sum of the pixels in image
K=sume of the pixels in k-space
K space is the spatial frequency domain
In Y direction the same is true (ky=1/ Δy) or Δky=1/FOVy

35. The relation between phase and frequency is:
Θ=∫ωdt
ω=γ.B= γ.G.x
Θy= ωy.ty= γ.By.ty= γ.Gy.y.ty= (γ.Gy.ty)y=ky.y

36. Scan parameters and Optimization
Chapter 17
Scan parameters and Optimization

37. Scan parameters Primary parameters (are set directly) and are:
A) contribute to image contrast: TR TE TI
FA (flip angle)
B) Contribute to coverage
Slice thickness
Interslice gap
C) Contribute to resolution
FOV (in x and y direction) Nx Ny
NEX
Bandwidth

38. Scan parameters
From the primary parameters we can get secondary parameters which are:
1) S/N
2) Resolution
3) Coverage
5) Scan time
6) Image contrast

39. SNR (signal to noise ratio)
SNRα (voxel volume) {(Ny)(NEX)/BW}1/2
NEX (number of excitation)
NEX => SNR by (NEX)1/2
BW => SNR
BW=N (number of pixel in x direction)/Ts (read out or sampling time) example 256/8=32KHz
(S1+S2)/(N1+N2)=2S/(2)1/2N=(2)1/2S/N

40. SNR increase by doing the following:
1)increasing TR
2)Decreasing TE
3)Using lower BW (by BW-1/2)
4)Using volume imaging
5)Increasing NEX (by NEX1/2)
6)Increasing Ny (by Ny 1/2)
7)Increasing voxel size

41. SNR in 3D SNRα (voxel volume) {(Nz)(Ny)(NEX)/BW}1/2
SNR(in 3D) α (Nz)1/2SNR(in 2D)
1/BW=Ts/Nx=>
SNRα (voxel volume) {(Ny)(NEX)(Ts)/Nx}1/2
T=Ts.Ny.NEX=>
SNR α(voxel volume)(total sampling time of all the signals) 1/2

42. Resolution
It is determined by :
1-Pixel size=FOV/No. of pixels
Ny =>better Res.
2-Total sampling time
Acquisition time
Scan time=TR.Ny.NEX
FSE time=TR.Ny.NEX/ETL
In 3D:
Time=TR.Ny.Nz.NEX

43. Coverage (distance covered by multislice acquisition)
1) Increase if:
>>Increase slice thickness
>>increase interslice gap
>>Increase TR or decrease the last TE (i.e. Increase TR/TE)
>>Decrease sampling time Ts (resulting in lower TE)
2) Coverage increase if:
>>Increase TE
>>Increase Ts
>>Increase ETL in FSE imaging (due to longer final TE)
3)Increase interslice gap causes:
>>Increase coverage
>>Decrease cross-talk artifact
>>Increase SNR (due to increasing effective TR by reducing cross-talk)
>>Decrease detection of small lesions (which may lies within the gap)

44. What happens if we increase or decrease TR
1) Increasing TR:
Increase SNR (according to T1 recovery curve)
Increase coverage (more slice)
Decrease T1W image
Increase PD and T2 weighting
Increase scan time
2)Decreasing TR:
Decrease SNR
Decrease coverage
Increase T1W
Decrease PD and T2 weighting

45. What happens if we change TE
1) Increasing TE:
Increase T2W
Increase dephasing and thus decrease SNR (according to t2 decay curve)
Decrease number of possible slice (decrease coverage)
No change in scan time
2)Decreasing TE:
Decrease T2W or PDW
Increase SNR (less dephasing)
Increase coverage

46. TI (inversion time) Advantages:
Can suppress various tissue by selecting appropriate TI
1-STIR when TI=0.693T1(fat)
2-FLAIR when TI=0.693T1(fluid)
Disadvantages:
1-Decrease SNR
2-Decrease coverage (by a factor of about 2 due to presence of the extra 180 degree pulse)